UNIVERSITI PUTRA MALAYSIA DIELECTRIC PROPERTIES OF ND-DOPED YTTRIUM IRON GARNET AND CU OR CO-DOPED NICKEL ZINC FERRITES KHE CHENG SEONG. FS 2006 13
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UNIVERSITI PUTRA MALAYSIA
DIELECTRIC PROPERTIES OF ND-DOPED YTTRIUM IRON GARNET AND CU OR CO-DOPED NICKEL ZINC FERRITES
KHE CHENG SEONG.
FS 2006 13
DIELECTRIC PROPERTIES OF Nd-DOPED YTTRIUM IRON GARNET AND CU OR CO-DOPED NICKEL ZINC FERRITES
By
KHE CHENG SEONG
Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of the Requirements for the Degree of Master of Science
January 2006
DEDICATION
I would like to dedicate this thesis to family members and all my friends.
Abstract of thesis presented to Senate of Universiti Putra Malaysia in fulfilment of the requirements for the degree of Master of Science
DIELECTRIC PROPERTIES OF Nd-DOPED YTTRIUM IRON GARNET AND CU OR CO-DOPED NICKEL ZINC FERRITES
KHE CHENG SEONG
January 2006
Chairman :Jumiah Binti Hassan, PhD
Faculty
In this work, three series of soft ferrites were synthesized via solid state route. These
are Nio.3-xCu,Zno.7Fe204 (x= 0.0, 0.05, 0.10, 0.15, 0.20, 0.25 and 0.30), Ni0.S-
.C&Zno.~Fe204 (x=O.O, 0.1, 0.2, 0.3, 0.4, and 0.5) and Y3..NdxFes0~2 (x=O.O, 0.4,
0.8, 1.2 and 1.6). The X-ray diffraction patterns showing single phases for these three
samples series, confirmed that the spinel and garnet structure had been formed in the
Ni-Zn ferrites and YIG respectively.
Ni-Zn ferrites substituted with copper oxide showed exaggerated grain growth
whereas the other series substituted with cobalt oxide had no massive changes in the
microstructure. For the YIG substituted with neodymium oxide, the first sample
exhibited a porous microstructure and developed to become a more compact and
poreless microstructure as neodymium increased.
Measurement of the electrical properties was carried out in the temperature range
from 28°C to 300°C in the low frequency region of 10 Hz to 1 MHz. Impedance
analyzer was employed in the ac data acquisition whereas a pico-ammeter and a dc
voltage source were used to measure electric current at different voltages.
The results obtained from dielectric measurements indicate that microstructure of the
samples plays an important role in the dielectric dispersion. A sample with higher
porosity is associated with a low value of dielectric permittivity due to its high
resistivity. Meanwhile a sample with a more compact structure exhibits higher
dielectric permittivity due to its higher conductivity. Hence, electron hopping
between ~ e ~ + and ~ e ~ ' would increase in the conductive sample and give higher
dielectric permittivity if compared with the resistive one.
The dielectric response for every sample in the three series of soft ferrites displayed
different mechanisms throughout the investigated temperature range. Therefore,
dielectric behaviour of a sample can be modeled into at least two equivalent circuits.
The complex impedance plots of both samples Ni-Zn ferrites and YIG showed
overlapping semicircles. However, at high temperature the high frequency arc
disappeared and there remained just one semicircle. The center of the semicircle for
all samples was depressed below the real impedance axis and described by the
parameter a. The results indicate that all these three series of soft ferrites can be
represented by two parallel RC circuits connected in series that correspond to the
contributions of grain and grain boundary.
The ac conductivity for the three series of soft ferrites showed almost similar
behaviour. At lower temperature, the ac curves can be divided into two region. The
kWlPW1;AW %TAN ABWX SMMj ti!lwmmmwm
low frequency region showed that the ac conductivity was weakly dependent on
frequency whereas at high frequency region, it was strongly dependent on frequency.
As the temperature increased, the ac conductivity seemed independent of frequency.
Extrinsic and intrinsic conductions had been inferred to occur in these samples.
It is also found that microstructural entities such as grains and porosity play an
important role in the dc resistivity. The two activation energies obtained indicated
that there were probably two parallel conduction mechanisms or spin reorientation
phase transition occurred.
Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains
SIFAT DIELEKTIUK GARNET BESI YTTRIUM YANG DIDOPKAN DENGAN Nd DAN FERIT NIKEL ZINK YANG DIDOPKAN DENGAN
Cu ATAU Co
Oleh
Pengerusi
Fakulti
KHE CHENG SEONG
January 2006
: Jumiah binti Hassan, PhD
:Sains
Dalam kajian ini, tiga siri ferit lembut telah disediakan melalui tindak balas keadaan
pepejal. Ferit yang dimaksudkan adalah Nio.3.xCuxZno.7Fe204(x= 0.0, 0.05, 0.10,
0.15,0.20, 0.25 and 0.30), Nio 5.,Co,Zno.5Fez04(x=0.0, O.1,0.2, 0.3, 0.4, and 0.5) dan
Y3-xNdxFe5012(x=0.0, 0.4, 0.8, 1.2 and 1.6). Pembelauan sinar-x mengesahkan
kesemua sampel dalam fasa tunggal dengan struktur spinel dm garnet.
Nio,3,CuxZno.7Fe204 didapati mengalami proses pertumbuhan butiran yang ketara
manakala N i 0 . ~ - , C ~ Z n ~ . s F e ~ 0 ~ tiada perubahan yang ketara dalam mikrostruktur.
Untuk Y3-xNdxFes012, pada mulanya menunjukkan liang yang banyak tetapi
kemudian menjadi semakin tumpat dan kurang liang apabila kandungan neodymium
meningkat.
Pengukuran sifat elektrik telah dilakukan pada julat suhu diantara 28°C dan 300°C
pada fiekuensi rendah daripada 10 Hz hingga 1 MHz. Mesin analisis impedans telah
digunakan untuk memperolehi data ac manakala piko ammeter dan punca voltan dc
digunakan untuk pengukuran arus terus pada voltan yang berlainan.
Daripada sifat dielektrik yang diperolehi, didapati mikrostruktur memainkan peranan
yang penting. Sampel yang mempunyai liang yang banyak mempunyai nilai dieletrik
yang rendah. h i disebabkan sampel yang mempunyai lebih keliangan mempuyai
tanga an yang lebih besar dan seterusnya melarang elektron yang melompat di
antara ~ e ~ + dan ~ e ~ + y a n g menyebabkan polarisasi dalam ferit.
Sifat dielektrik untuk setiap sampel dalam tiga siri ferit ini menunjukkan mekanisma
yang berlainan pada suhu yang berbeza. Jadi, satu sampel biasanya boleh diwakili
oleh sekurang-kurangnya dua model litar setara dalam julat suhu kajian ini.
Komplek impedans untuk ketiga-tiga sampel ferit lembut menunjukkan dua lengkung
semibulatan bertindih. Akan tetapi, pada suhu yang tinggi, lengkung semibulatan
pada fi-ekuensi yang tinggi lenyap dan meninggalkan hanya satu lengkung
semibulatan. Semua sernibulatan mempunyai pusat yang tertekan ke bawah paksi
nyata impedans. Keputusan menunjukkan kebanyakan sampel boleh diwakili oleh
dua litar RC yang selari disambung secara siri yang disebabkan oleh butiran dan
sempadan butiran sampel.
Konduktiviti ac untuk ketiga-tiga siri sampel hi menunjukkan kelakuan yang agak
sama. Pada suhu yang rendah, lengkung ac boleh dibahagkan kepada dua bahagian.
Pada bahagian fiekuensi rendah, kekonduksian ac bergantung lemah terhadap
fiekuensi manakala pada fiekuensi tinggi, ia bergantung kuat kepada fiekuensi.
Apabila suhu meningkat, kekonduksian ac hampir tidak bergantung kepada
fiekuensi. Kekonduksian ektrinsik dan intrinsik dipercayai berlaku dalam sampel-
sampel ini.
vii
Mikrostruktur seperti butiran dm liang didapati memainkan peranan yang penting
dalam kekonduksian arus terus. Dua tenaga pengaktifan diperolehi dipercayai
disebabkan oleh kewujudan dua mekanisma kekonduksian yang selari atau fasa
translasi putaran reorientasi telah berlaku.
ACKNOWLEDGEMENT
First and foremost, I would like to express my highest gratitude to Dr. Jurniah
Hassan, as my project supervisor, Assoc. Prof. Dr. Wan Mohd Daud Wan Yusoff and
Assoc. Prof. Dr. Mansor Hashim as my co-supervisors for giving the guidance,
suggestions and knowledge in the dielectric theories and also in the femte materials.
I would like to thank Mr. Woon, lecturer from UNITEN, my lab-mate, Tay, Walter
Charles, INFOPORT staff, XRD lab assistant and many others who had help me
through out this project where without their invaluable help this project could not
have been completed with success.
I also would like to acknowledge Universiti Putra Malaysia for the financial support
under the PASCA scheme.
Finally, I would like to express my fullest appreciation to my family members
especially to my parents for their support and understanding from the very beginning
of my work until this studies were completed.
1 certify that an Examination Committee has met on 25" January 2006 to conduct the final examination of Khe Cheng Seong on his Master of Science thesis entitled "Dielectric Properties of Nd-Doped Yitrium Iron Garnet and Cu- or Co-Doped Nickel Zinc Ferrites" in accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree) Regulations 1981. The Committee recommends that the candidate be awarded the relevant degree. Members of the Examination Committee are as follows:
MOHD. MAAROF H.A MOKSIN, PhD Professor Faculty of Science Universiti Putra Malaysia (Chairman)
ABDUL HALIM SHAARI, PhD Professor Faculty of Science Universiti Putra Malaysia (Internal Examiner)
ZAIDAN ABDUL WAHAB, PhD Associate Professor Faculty of Science Universiti Putra Malaysia (Internal Examiner)
IBRAHIM ABU TALIB, PhD Professor Faculty of Science and Technology Universiti Kebangsaan Malaysia (External Examiner)
School of ~raddate Studies Universiti Putra Malaysia
Date:
This thesis submitted to the senate of Universiti Putra Malaysia and has been accepted fulfilment of the requirement for the degree of Master of Science. The members of the Supervisor Committee are as follows:
JUMIAH HASSAN, PhD Lecturer Faculty of Science Universiti Putra Malaysia (Chairman)
WAN MOHD. DAUD WAN YUSOFF, PhD Associate Professor Faculty of Science Universiti Putra Malaysia (Member)
MANSOR HASHIM, PhD Associate Professor Faculty of Science Universiti Putra Malaysia (Member)
AINI IDERIS, PhD Professor/Dean School of Graduate Studies Universiti Putra Malaysia
Date: 13 APR 2006
DECLARATION
I hereby declare that the thesis is based on my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions.
xii
TABLE OF CONTENTS Page
EDICATION 3STRACT BSTRAK 2KNOwLEDGEMENT 'PROVAL ECLARATION :ST OF TABLES :ST OF FIGURES :ST OF PLATES :ST OFABBREVIATIONS
CHAPTER
INTRODUCTION 1 . 1 Introduction 1.2 Objectives 1.3 Research Overview
LITERATURE REVIEW 2.1 Dielectric Properties of Solid 2.2 Dielectric Properties of Ferrites 2.3 AC Electrical conductivity 2.4 DC Electrical conductivity
3 THEORY 3.1 Spinel Structure 3.2 Garnet Structure 3.3 Dielectric Definition 3.4 Dielectric Polarization 3.5 Dielectric Models
3.5.1 Debye Expression 3.5.2 Cole-Cole Expression 3.5.3 Power Law Relation Alternating Current Conductivity Complex Plane Analysis DC conductivity
4 METHODOLOGY 4.1 Sample Preparation 4.2 AC Measurement 4.3 DC Measurement 4.4 Structure Analysis 4.5 Microstructural Analysis 4.6 Density
. . 11 ... 111
vi iv v xii xv xix XXV
xxvi
... Xl l l
RESULTS AND DISCUSSION X-Ray Diffraction Patterns 5.1.1 Nickel Zinc Ferrites Substituted With Copper 5.1.2 Nickel Zinc Ferrites Substituted With Cobalt 5.1.3 Yttrium Iron Garnet Substituted With Neodymium Microstructural Analysis 5.2.1 Nickel Zinc Ferrites Substituted With Copper 5.2.2 Nickel Zinc Ferrites Substituted With Cobalt 5.2.3 Yttrium Iron Garnet Substituted With Neodymium Dielectric Properties in Frequency Domain 5.3.1 Nickel Zinc Ferrites Substituted With Copper
5.3.1.1 Negativecapacitance 5.3.2 Nickel Zinc Ferrites Substituted With Cobalt 5.3.3 Yttrium Iron Garnet Substituted With Neodymium Dielectric Response with Equivalent Circuit Modeling 5.4.1 Nickel Zinc Ferrites Substituted With Cobalt 5.4.2 Nickel Zinc Ferrites Substituted With Copper 5.4.3 Yttrium Iron Garnet Substituted With Neodymium Complex Impedance Plot 5.5.1 Nickel Zinc Ferrites Substituted With Copper 5.5.2 Nickel Zinc Ferrites Substituted With Cobalt 5.5.3 Yttrium Iron Garnet Substituted With Neodymium AC Conductivity In Frequency Domain 5.6.1 Nickel Zinc Ferrites Substituted With Copper 5.6.2 Nickel Zinc Ferrites Substituted With Cobalt 5.6.3 Yttrium Iron Garnet Substituted With Neodymium DC Resistivity 5.7.1 Nickel Zinc Ferrites Substituted With Copper 5.7.2 Nickel Zinc Ferrites Substituted With Cobalt 5.3.3 Yttrium Iron Garnet Substituted With Neodymium
CONCLUSION AND SUGGESTION 6.1 Conclusions 6.2 Suggestions
REFERENCES
APPENDICES
BIODATA OF THE AUTHOR
xiv
LIST OF TABLES
Table
3.1
Page
29 Capacitance values and their possible interpretation.
Starting materials for preparing yttnum iron garnet.
Starting materials for preparing nickel zinc ferrites.
Yttrium iron garnet substituted with neodymium ( Y , - ~ N ~ ~ F ~ ~ O ~ ~ )
Nickel zinc ferrites substituted with copper (Nio.3-xCuxZno.7Fe204)
Nickel zinc ferrites substituted with cobalt (Ni0.5,C~xZ~,5F~04)
Density and average grain size of nickel zinc ferrites substituted with copper.
Average grain size and density of nickel zinc ferrites substituted with cobalt.
Density and average grain size of YIG substituted with neodymium.
Activation energies of peak frequency for sample N1 to N7.
Activation energies of loss peak fi-equency, Fp for different samples.
Activation energy of Fp for samples Y 1 to Y5.
Theoretical values for fitting the experimental data for sample CC from(a) 28°C to 150°C (b) 200°C to 300°C.
Theoretical values for fitting the experimental data for sample C 1 fiom (a)2g°C to 1 00°C (b) 150°C to 300°C.
Theoretical values for fitting the experimental data for sample C3 fiom (b)28"C to 200°C (b) 250and 300°C.
Theoretical values for fitting the experimental data for sample C4 fiom (a)28"C to 50°C (b) 100°C to 300°C.
Theoretical values for fitting the experimental data for sample C5 fiom (a)28"C to 100°C (b) 150°C to 300°C.
Theoretical values for fitting the experimental data for sample C2 from 28°C to 300°C.
Theoretical values for fitting the experimental data for sample N1 from (a) 28°C to 100°C (b) 150°C to 300°C.
Theoretical value for fitting the experimental data for sample N2 fi-om (a) 28°C to 150°C (b) 200°C to 300°C.
Theoretical values for fitting the experimental data for sample N3 at (a) 28°C (b) 50°C to300°C.
Theoretical values for fitting the experimental data for sample N6 fiom (a) 28°C to 100°C (b) 150°C to 300°C.
Theoretical values for fitting the experimental data for sample N7 fiom (a) 28°C to 1 50°C (b) 200°C to 300°C.
Theoretical values for fitting the experimental data for sample N4 from (a) 28°C to 100°C (b)150° to 200°C (c) 250°C to 300°C.
Theoretical values for fitting the experimental data for sample N5 fi-om (a )28"C and 100°C (b) 150°C to 250°C.
Theoretical values for fitting the experimental data for sample Y1 from (a) 28°C to 150°C (b) 200°C to 300°C.
Theoretical values for fitting the experimental data for sample Y2 fiom (a) 28°C to 50°C (b) 100°C to 300°C.
Theoretical values for fitting the experimental data for sample Y3 fiom (a) 28°C to 200°C (b) 250°C and 300°C.
Theoretical values for fitting the experimental data for sample Y4 fiom (a)2g°C to 150°C (b) 200°C and 300°C.
Theoretical values for fitting the experimental data for sample Y5 fiom (a) 28°C to 150°C (b) 200°C to 300°C.
Values of fitted parameters for different samples at room temperature.
Theoretical values for fitting the experimental data of sample N4 at (a) 50°C to 100°C (b) 150°C to 300°C.
Theoretical values for fitting the experimental data of sample N5 at (a) 50°C to 150°C (b) 200°C to 300°C.
Theoretical values for fitting the experimental data of sample N1 at (a) 50°C and (b) 100°C to 300°C.
xvi
Theoretical values for fitting the experimental data of sample N2 at (a)50°C and (b)lOO°C to 300°C.
Theoretical values for fitting the experimental data of sample N3 from 50°C to 300°C.
Theoretical values for fitting the experimental data of sample N6 at (a)50°C to 100°C (b) 150°C to 300°C.
Theoretical values for fitting the experimental data of sample N7 at (a)50°C to 100°C (b) 150°C to 300°C.
Values of capacitance and resistance and the other parameters obtained fiom fitting for different samples at room temperature. 149
Theoretical values that used to fit the experimental data of sample C1 at (a) 50°C (b) 100°C to 300°C.
The resistances and the capacitances that obtained from the curve fitting for different samples at various temperatures.
Value of fitted parameters for sample Y2 fiom (a) 28°C to 100°C (b)150°C to 300°C
Theoretical values for fitting the experimental data for sample Y5 from 28°C to 300°C.
Theoretical values for fitting the experimental data for sample Y1 from (a) 28°C to 100°C (b) 150°C to 300°C
Theoretical values for fitting the experimental data for sample Y3 fkom (a) 28°C and 50°C (b) 100°C to 300°C.
Theoretical values for fitting the experimental data for sample Y4 from (a) 28°C to 150°C and (b) 200°C to 300°C.
Values of resistance and capacitance for sample Y 1 to Y5 at room temperature.
Activation energies of different samples at low and high temperature regions.
Activation energies of different samples at low and high temperature regions.
xvii
Activation energies of different samples at low and high temperature regions.
Activation energies of samples N1 to N7.
Activation energy calculated from Figure 5.78.
Activation energy of different samples.
xviii
LIST OF FIGURES
Figure
3.1
3.2
3.3
3.4
Page
13 Spinel structure.
Garnet structure.
Various types of polarization.
The probable occurrence of the various types of the polarization and the dependence of the permittivity with respect to frequency.
The frequency dependence of the real and imaginary parts of the permittivity of an Ideal Debye system corresponding to equation.
The frequency dependence of the real and imaginary parts of the permittivity corresponding to the Cole-Cole expression.
The bound dipolar dispersion.
The quasi-dc dispersion.
A schematic representation of the various observed types of dielectric response in the entire range of solids.
Equivalent circuit proposed for sample ferrites.
Sketch of a complex impedance plot showing various parameters.
The current of an ohmic material plotted versus the potential difference across it.
Procedure of sample preparation (Nio.3-,CuX 2110.7 Fe204).
Procedure of sample preparation (Nio.s-,Co, Zno.7 Fe204).
Procedure of sample preparation (YsxNdX FesOl2).
XRD patterns of nickel zinc ferrite substituted with copper.
XRD patterns of nickel zinc ferrites substituted with cobalt.
XRD patterns of yttrium iron garnet substituted with neodymium.
Diagrammatic representation the successive stages in the joining of two of grains by sintering.
Complex dielectric permittivity of samples N 1 to N7 at room temperature (a) dielectric permitivity (b) loss factor.
Dielectric properties of sample N2 at different temperature.
Arrhenius plot for sample N2.
Dielectric properties of samples N1 to N7 at 100°C.
Dielectric properties of samples N1 to N7 at 200°C.
Dielectric properties of samples N l to N7 at 300°C.
Dielectric permittivity of sample (a) N3 and (b) N5 at 300°C.
Dielectric properties for the nickel zinc femtes substituted with cobalt at room temperature with different composition.
Dielectric permittivity of sample CC plotted at various temperatures with the curve vertically shifted to avoid overlapping.
Arrhenius plot of the loss peak frequency, Fp of sample CC.
Dielectric properties of sample C1 at different temperature.
Dielectric properties for the nickel zinc ferrites substituted with cobalt at 100°C with different composition.
Dielectric properties for the nickel zinc ferrites substituted with cobalt at 200°C with different compositions.
Dielectric properties for the nickel zinc ferrites substituted with cobalt at 300°C with different compositions. Solid line has a gradient of -1.
Dielectric properties of sample Y 1 to Y5 at room temperature.
Loss factor for different samples with the curves vertically shifted up at room temperature.
A series of dielectric response of sample Y4 in the
temperature range from 28°C to 300°C.
Activation Energy of samples YIG obtained from peak maximum at low frequency (LP) and high fiequency (HP).
Effect of temperature on (a)dielectric permittivity (b)loss
factor of sample Y5. The solid line has a gradient of -1.
Dielectric permithvity versus frequency for sample Y1 to Y5 at 100°C
Dielectric permittivity versus frequency for sample Y 1 to Y5 at 200°C
Dielectric permittivity versus fiequency for sample Y 1 to Y5 at 300°C
Dielectric response of sample CC at various temperatures.
Equivalent circuit representing the dielectric response for the sample CC fiom temperature 28°C to 150°C.
Equivalent circuit representing the dielectric response for the sample CC fiom temperature 200°C to 300°C.
Dielectric response of sample C2 at various temperatures.
Equivalent circuit representing the dielectric response in the sample C2 fi-om temperature 28°C to 300°C.
Dielectric behaviour of sample N1 at various temperatures.
Dielectric behaviour of sample N2, N3, N6 and N7 at room temperature.
Dielectric response of sample N4 at various temperatures.
Equivalent circuit representing the dielectric response in the
sample N4 fiom temperature 28°C to 1 50°C.
Equivalent circuit representing the dielectric response in the sample N4 fiom temperature 250°C to 300°C.
Dielectric response of sample N5 at various temperatures.
Equivalent circuit represented the dielectric response in the sample N5 fiom temperatures 28°C to 100°C
Dielectric response of sample Y 1 at various temperatures.
xxi
Equivalent circuit represented the dielectric response in the sample Y 1 fiom temperature 200°C to 300°C
Dielectric response of sample Y5 at various temperatures.
Equivalent circuit representing the dielectric response in the sample Y5 fiom temperature 28°C to 150°C
Equivalent circuit representing the dielectric response in the sample Y5 fiom temperatures 200°C to 300°C
Complex impedance plot of samples N1 to N4 at room temperature.
Complex impedance plot of samples N5 to N7 at room temperature.
Exploded view of impedance plot at high frequencies for sample N 1 to N7 at room temperature.
Equivalent circuit used to represent the electrical properties in samples N1, N2, N4, N5, N6 and N7 at room temperature.
Equivalent circuit used to represent the electrical properties of in samples N3.
Complex impedance plots for sample N1 at different temperature.
Impedance Z spectroscopic plot for sample N1 at different temperatures.
Modulus M" spectroscopic plot for N1 at different temperatures.
Impedance plot for different samples at room temperature.
Resistance of samples CC to C5 at room temperature obtained fi-om impedance plot at low fiequency end.
Exploded view of the different samples at room temperature at high fiequency region.
Equivalent circuit used to represent the electrical properties in different samples at room temperature.
xxii
Complex impedance plot for the sample C 1 at different temperatures.
Equivalent circuit used to represent the series resistance and grain boundary effects in sample C 1 at temperature 100°C and above.
The invariant of the capacitance of the sample C1 at different temperatures.
Complex impedance plot of samples Y2 at various temperatures.
Equivalent circuit used to represent sample Y2 fiom 28°C to 100°C.
Equivalent circuit used to represent sample Y2 fiom 150°C to 300°C.
Complex impedance plots of sample Y5 at various temperatures.
Equivalent circuit used to represent sample Y5 at various temperature.
Ac conductivity of different samples at room temperature.
Ac conductivity of sample N1 at different temperatures.
Arrhenius plot of sample N1.
AC conductivity of different samples at room temperature.
Ac conductivity of sample CC at different temperatures.
Arrhenius plot of sample CC at 10 Hz.
AC conductivity of different samples at room temperature.
AC conductivity of sample Y 1 at various temperatures.
Arrhenius plot of sample Y 1 at 10 Hz.
DC resistivity of nickel zinc ferrites substituted with copper with different composition at room temperature.
Resistivity of samples (a) N1 to N4 and (b) N5 to N7 at different temperatures.
D.C Resistivity of nickel zinc femtes substituted with copper with respect to reciprocal temperature.
Resistivity of samples CC to C5 at various temperatures.
Resistivity of samples CC to C5 at room temperature.
Arhenius plot of dc resistivity of sample CC to C5.
DC resistivity of YIG substituted with neodymium.
Arrhenius plot for sample Y 1 to Y5.
xxiv
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